Consider a round jar with no lid. The radius of the opening in the jar is 10. A coin (with a radius R < 10) can be placed flat on the edge of the jar without falling. The coin can be placed such that its center is on the rim of the jar, or it can be moved toward the center of the jar.

What is R, when the coin is as close to the center of the jar as possible without falling in, and the inside edge of the coin is at the center of the jar's opening?